Solve for $x$ : $2x^2 + 2x - 144 = 0$
Dividing both sides by $2$ gives: $ x^2 + {1}x {-72} = 0 $ The coefficient on the $x$ term is $1$ and the constant term is $-72$ , so we need to find two numbers that add up to $1$ and multiply to $-72$ The two numbers $9$ and $-8$ satisfy both conditions: $ {9} + {-8} = {1} $ $ {9} \times {-8} = {-72} $ $(x + {9}) (x {-8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -8) = 0$ $x + 9 = 0$ or $x - 8 = 0$ Thus, $x = -9$ and $x = 8$ are the solutions.